I'm trying to make as simple a system as possible, so here's the thought:

When making the character, you choose whatever he is good and bad at. For any action, you roll two six-sided dice (2d6), one less if it's something you're bad at, one more if it's something you're good at.

Target numbers for static obstacles would go as follow:

3 - A trivial task anybody can accomplish.
5 - A simple task.
7 - Not too complex, but best left to experts.
9 - An actual challenge.
11 - Should be avoided by people who don't know what they're doing.
13 - Impressive by any standards.
15 - Commonly believed to be impossible.

As for contested actions between characters, both would roll and the result would depend on the difference:

1 or less - Results inconclusive, nothing achieved by either side.
from 2 to 5 - A strike marked against the lowest result. Three strikes and the character has lost the conflict.
6 or more - Immediate victory for the higher scorer.

I don't pretend at balance, but perhaps this'll work well enough to resolve a problem quickly.